Question

Where are the x-intercepts for f(x) = −4cos(x − pi over 2 ) from x = 0 to x = 2π?

Answer 1

@DanJS

Answer 2

Have you considered substituting f(x) = 0?

Answer 3

Yes, I just don't know how to simplify with the "cos" value in the equation; it's really confusing.

Answer 4

You don't simplify cos(x). Why are you trying to do that? You know things about it.

−4cos(x − pi/2 ) = 0

-4 is of no consequence for this problem. This leaves:

cos(x − pi/2 ) = 0

Where is cos(x) = 0? You answer this question. Tell me EVERYWHERE this is the case.

Answer 5

Hmm, I still don't understand. :/

Answer 6

Simple question. Ignore that there is a different question. Just answer this question.

Fundamental knowledge of the cosine function.

Where is cos(x) = 0? It is a periodic function. It takes on the value zero infinitely many times. Where are all these times? They are very regular and can be stated rather succinctly.

Answer 7

I'm sorry, I really don't know. @tkhunny

Answer 8

That's not acceptable. I am sure you know that \(\cos(\pi/2) = 0\). I am sure you know that \(\cos(3\pi/2) = 0\). I am relatively sure you know that \(\cos(-\pi/2) = 0\).

Those are just three of the infinitely many values where this is so. What are the rest of the values. You MUST know them all in order to have a sufficient understanding of the cosine.

Answer 9

How in the world will I determine any of these functions?

Answer 10

@tkhunny

Answer 11

**I mean values

Answer 12

You must study the properties.

Here's a 10 minute video that is helpful. https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/unit-circle-definition-of-trig-functions/v/unit-circle-definition-of-trig-functions-1

Answer 13

the symmetry of things on that circle is useful , like Cos(-angle) = Cos(+angle), x value stays the same...

with that you can write cos(theta - pi/2) = cos( pi/2 - theta)

the cosine of pi/2 - theta, is the same as the sine value of the angle theta, cosine of an angle is the same as the sine of the angle compliment , like sin(12) = cos(78),



if you can remember those kinds of things, then the problem is reduced to figuring
when the sin(theta) = 0